The effect of idealized water waves on the turbulence structure and kinetic energy budgets in the overlying airflow

The influence of an idealized moving wavy surface on the overlying airflow is investigated using direct numerical simulations (DNS). In the present simulations, the bulk Reynolds number is Re = 8000 (; where U₀ is the forcing velocity of the flow, h the height of the domain and v the kinematic viscosity) and the phase speed of the imposed waves relative to the friction velocity, i.e., the wave age varies from very slow to fast waves. The wave signal is clearly present in the airflow up to at least 0.15λ (where λ is the wave length) and is present up to higher levels for faster waves. In the kinetic energy budgets, pressure transport is mainly of importance for slow waves. For fast waves, viscous transport and turbulent transport dominate near the surface. Kinetic energy budgets for the wave and turbulent perturbations show a non-negligible transport of turbulent kinetic energy directed from turbulence to the wave perturbation in the airflow. The wave-turbulent energy transport depends on the size, tilt, and phase of the wave-induced part of the turbulent Reynolds stresses.According to the DNS data, slow waves are more efficient in generating isotropic turbulence than fast waves.Despite the differences in wave-shape as well as in Reynolds number between the idealized direct numerical simulations and the atmosphere, there are intriguing similarities in the turbulence structure. Important information about the turbulence above waves in the atmosphere can be obtained from DNS—the data must, however, be interpreted with care.     

Microscale ordered motions and atmospheric structure associated with thin echo layers in stably stratified zones

The interpretation of ultra-high resolution radar observations of thin clear-air echo strata is made with the aid of fine-scale aircraft measurements. The echo layer, generally comprising two sub-strata each 5 m thick and spaced 7–10 m apart, is found within a 10–20 m deep section of a strong inversion where the thermal stability and shear are maximized, and the Richardson number is close to 0.25. Mechanical turbulence is restricted entirely to this layer; the variance of the N-S velocity component, ³, is the strongest, consistent with the orientation of the shear vector in this stratum. Spectra and cospectra of a 9-s slant run through the echo stratum show remarkably ordered motions. A strong negative peak of <w> covariance at 80-m scale, accompanied by a zero of <uw> covariance and bulges in the longitudinal () and vertical (w) velocity spectra, is identified with breaking Kelvin-Helmholtz waves oriented in the N-S direction along the shear vector. A synthesis of the temperature and velocity structures from measurements along the flight path confirms the ordered motion deduced from the spectra and reveals a group of K-H waves of 80-m length and 10-m height at the height of the radar echo. Microscale K-H ripples of 3–4 m length are also deduced to be present in the 0.5 m thick interfacial region where the thermal gradient and shear are strongly enhanced by the larger shearing K-H wave.Two possible sources of the echoes are proposed: (1) scatter from fully developed turbulence within the interfacial zone in an inertial subrange falling entirely in sub-meter scales; and (2) the incoherent summation of specular reflections from properly oriented portions of the microscale K-H ripples. While the authors favor the first of these mechanisms, both require stringent conditions of the physical microstructure which are beyond the available observations. Fossil turbulence is precluded as an echo mechanism.This paper is based in part on the doctoral dissertation by the senior author.Present affiliation: Air Force Cambridge Research Laboratories, Bedford, Mass., U.S.A.     

Turbulence in stably stratified fluids: A review of laboratory experiments

This is a review of laboratory studies of mixing in stably stratified fluids away from the direct intluence of boundary layers, and was written to introduce the session on laboratory experiments at the IUCRM Colloquium.Internal waves (Section 2) can lead to turbulence by creating regions of unstable density gradients through their mutual interactions, by individually breaking by forming rotors, and by reducing the local Richardson number until Kelvin-Helmholtz instability results. They may be important in radiating energy from turbulent or spreading regions. Critical-layer absorption of internal waves is not found to be a direct cause of turbulence in experiments with 15 Richardson number 5, although the modification of the vertical density profile may be significant.Turbulent-laminar interfaces without mean shear (Section 3) and with mean shear (Section 4) are described. The source of turbulence in these experiments is partly external, either generated by an oscillating grid or by a (relatively) moving boundary. The development of turbulence generated entirelywithin a stratified layer by Kelvin-Helmholtz instability, is described in detail in Section 5, and the results are compared with measurements in the ocean and in the atmosphere.     

Radar and sodar probing of waves and turbulence in statically stable clear-air layers

This paper reviews the remote sensing of waves and turbulence in statically stable atmospheric layers, utilizing sodar and microwave radar echoes from the small-scale inhomogeneities in gaseous refractive index caused by localized fluctuations in temperature, humidity, and velocity. Scattering theory and sounding methodology are reviewed briefly, and the relative performance of typical radar and sodar systems compared. The main section of the paper takes the form of a summary and discussion of experimental progress since 1969, showing how the echo patterns obtained may be applied to the interpretation of multiple layering, gravity waves, internal fronts and the details of dynamic instability and the genesis of turbulence in stably stratified shear layers. In addition, methods for the measurement of the intensity of the small-scale ( /2) variability of wind, temperature and water vapor from the observed radar or sodar echo intensities, and the use of Doppler techniques for the measurement of mean velocity and turbulence are discussed.SODAR from SOund Detection And Ranging in analogy to RAdio Detection And Ranging.     

Observations of the energy-containing oceanic Eddies,and theoretical models of waves and turbulence

Two of the best available observed frequency spectra of energy-containing oceanic motions are summarized. Without provoking any simple explanation, they affirm that an efficient, homogeneous cascade of energy to small scales isnot occurring. The way is left open for interpretation as a mixture of geostrophic turbulence and waves.Detailed models are given which yield plausible behavior of various parts of the wave-number and frequency spectra, and illustrate the workings of nonlinearity and wave dispersion: (i) simple dispersion of linear, wind-generated internal waves gives at depths an inertial peak and a steeply sloping high-frequency spectrum (the inertial peak at the very top of the ocean is a direct response of the mixed layer to the wind); (ii) at longer periods,two-dimensional turbulence subjected to the beta effect produces well-ordered motions from a chaotic initial state, with dominant length and time-scale independent of initial conditions. The turbulence evolves quickly and naturally into Rossby waves, leaving a peaky, quasi-stationary spectrum; (iii) inone dimension, the Korteweg de Vries equation again shows how waves may sharpen and fix the wave-number spectrum while dispersing the energy in physical space; (iv) possible application of the ideas tothree-dimensional turbulence and waves is discussed.The most general result is that the scale-dependent boundary, at which the wave steepness is about unity, often divides energy-frequency/wave-number space into regions in which the mobility of energy is vastly different; depending on the direction and speed of nonlinear migration within these regions, energy may pile up at this boundary. Thus, wave-restoring forces can concentrate spectra at certain wave numbers while dispersing the fields in physical space.Now at Woods Hole Oceanographic Institution.     

Boundary-layer turbulence spectra in stable conditions

Simultaneous measurements of horizontal and vertical wind speeds and temperature fluctuations at heights up to 91 m in the stable atmospheric boundary layer are described. The power and cospectral shapes show a low-frequency peak (near the Brunt-Väisälä frequency) separated by a spectral gap from a peak at high frequency due to turbulence. Spectral shapes in the turbulence subrange at 8 m are in good agreement with the universal curves previously presented by Kaimal (1973). Further information is given on the variation of the scaling parameter, f ₀, with stability; and the applicability of the normalising procedure to the spectra from the higher levels is discussed.     

A generalized scaling for convective shear flows

During the last two decades, different scalings for convective boundary layer (CBL) turbulence have been proposed. For the shear-free regime, Deardorff (1970) introduced convective velocity and temperature scales based on the surface potential temperature flux,Q _s , the buoyancy parameter, , and the time-dependent boundary-layer depth,h. Wyngaard (1983) has proposed decomposition of turbulence into two components, bottom-up (b) and top-down (t), the former characterized byQ _s , the latter, by the potential temperature flux due to entrainment,Q _h . Sorbjan (1988) has devised height-dependent velocity and temperature scales for both b- and t-components of turbulence.Incorporating velocity shear, the well known similarity theory of Monin and Obukhov (1954) has been developed for the atmospheric surface layer. Zilitinkevich (1971, 1973) and Betchov and Yaglom (1971) have elaborated this theory with the aid of directional dimensional analysis for a particular case when different statistical moments of turbulence can be alternatively attributed as being of either convective or mechanical origin.In the present paper, we attempt to create a bridge between the two approaches pointed out above. A new scaling is proposed on the basis of, first, decomposition of statistical moments of turbulence into convective (c), mechanical (m) and covariance (c&m) contributions using directional dimensional analysis and, second, decomposition of these contributions into bottom-up and top-down components using height-dependent velocity and temperature scales. In addition to the statistical problem, the scaling suggests a new approach of determination of mean temperature and velocity profiles with the aid of the budget equations for the mean square fluctuations.Notation ATL alternative turbulence layer - CBL convective boundary layer - CML convective and mechanical layer - FCL free convection layer - MTL mechanical turbulence layer     

基于支持向量机的雷达地物回波识别研究

多普勒天气雷达探测过程中的非气象因子会显著影响雷达资料的定量化应用,在雷达基数据的应用前需对雷达资料进行抑制地物杂波、去距离折叠和退速度模糊等质量控制。本文在现有的自动识别地物回波方法的基础上,提出了基于支持向量机（Support Vector Machine,SVM）识别雷达地物杂波的方法,2013年6-8月对安庆和常州两地的CINRAD/SA雷达观测资料进行雷达地物回波识别,并将其与运用人工神经网络（Artificial Neural Networks,ANNs）识别的结果进行对比,结果表明支持向量机方法能够取得更好的效果。在地物、降水回波总样本识别和地物回波识别方面更为有效;降水回波的误判方面,神经网络略优于支持向量机,但两者差异不大,都将降水回波的误判率控制在了一个较小的范围内;另外支持向量机方法较之神经网络方法对于训练样本数目的依赖性较小,在训练样本较少时,支持向量机方法仍能保持有效的识别效果。     

Measurements of internal waves and turbulence in two-dimensional stratified shear flows

A turbulent stratified shear flow is generated in a towing tank by towing a grid or a circular cylinder through a tank of stratified salt water. The internal waves and turbulence generated in these flows are visualized with shadowgraphs and measured with quartz-coated hot-film probes (up to four probes for velocity fluctuations) and single-electrode conductivity probes (up to four probes for salinity fluctuations) which are towed at the same speed as the obstacle. The velocity and salinity signals are recorded on magnetic tapes. A portion of these signals is processed directly-on-line with a digital computer. From these shadowgraphs and probe measurements, we observe that

1. Far downstream of the obstacle where the turbulence has already subsided, the stratified fluid always has a layered structure. This layered structure persists for a long time, and is a result of the convection of turbulently mixed layers by the mean flow. These results indicate that in the regions of a stably stratified atmosphere and ocean where the turbulence has subsided, one could often find layered structure.
2. There are spectral peaks and valleys in the measured velocity and salinity autospectra when the stratifications are sufficiently strong. Under certain conditions, these spectral peaks tend to lift up the spectral curves to show substantialf ^?5/3 subranges, although the turbulence Reynolds numbers are too low for the flows to have recognizable inertial subranges. This anomalousf ^?5/3 subrange demonstrates the pitfalls of using spectral measurements in thef ^?5/3 subrange to predict the turbulent energy dissipation rate through the Kolmogorov hypothesis.
3. A diagnostic method is developed for distinguishing internal waves from turbulence, utilizing their phase characteristics. The phase characteristics can be conveniently examined from the cospectra and quadrature spectra measurements of: (a), two vertically separated velocity probes; (b), two vertically separated density probes; and (c), a velocity probe and a density probe. This method is demonstrated to be useful in the laboratory and can be applied directly to atmospheric and oceanic measurements to distinguish internal waves from turbulence.
4. From the coherency measurements, it is found that the entire turbulent stratified wake is actually whipping up and down at a frequency corresponding to the Brunt-Väisälä frequency. This indicates that similar stratified shear flows in the atmosphere and in the ocean, such as the jet streams in the atmosphere and the Cromwell current in the ocean, may oscillate vertically, which in turn can induce horizontal oscillation and meandering.

     

Phase-Averaged Flow Properties Beneath Microscale Breaking Waves

The phase-averaged characteristics of the turbulent velocity fields beneath steep short wind waves are investigated. A scheme was developed to compute the phase of individual wind waves using spatial surface displacement data. This information was used to analyze the two-dimensional velocity data acquired using particle image velocimetry (PIV) in a wind-wave tank. The experiments were conducted at a fetch of 5.5m and at wind speeds that ranged from 4 to 10ms⁻¹. Under these conditions previous studies have shown that a significant percentage of the waves are microscale breaking waves. An analysis of the phase-averaged results suggests under these conditions (short fetches and moderate wind speeds) a wind-driven water surface can be divided into three regions based on the intensity of the turbulence. These are the crests of microscale breaking waves, the crests of non-breaking waves and the troughs of all waves. The turbulence is most intense beneath the crests of microscale breaking waves. In the crest region of microscale breaking waves coherent structures were observed that were stronger and occurred more frequently than beneath the crests of non-breaking waves. Beneath the crests of non-breaking waves the turbulence is a factor of two to three times weaker and beneath the wave troughs it is a factor of six weaker. These findings provide additional support for the hypothesis that approximately two-thirds of the gas and heat fluxes occur across the turbulent wakes produced by microscale breaking waves.     

Evaluation and model impacts of alternative boundary-layer height formulations

We study bulk formulations for the boundary-layer height which are currently in use for atmospheric modelling. The formulations are based on various forms of the Richardson number, and these are evaluated with Cabauw field data in stable conditions. Results for both a large-eddy simulation model and anE-ε turbulence closure model for neutral boundary layers are also utilised. An updated formulation is introduced, which combines the effects of shear in the outer region of the boundary layer with surface friction. The updated formulation has a better performance for neutral boundary layers with upper level stratification. The findings are illustrated with a single-column model for a case with relatively high winds over the tropical ocean including shallow cumulus convection, and for a case with fair weather over land. We also show that for stable conditions, the updated formulation performs better than estimates on the basis of surface friction alone.     

Measurements of bubble plumes and turbulence from a submarine

Abstract

An experiment using turbulence probes and an array of side‐scan and vertically pointing pencil beam sonars mounted on the U.S. submarine Dolphin was carried out to measure turbulence in near‐surface regions of acoustic scattering, in particular, those caused by subsurface bubbles produced by breaking wind waves. The dataset collected during winds of 5–9 m s^?1 reveals the banded patterns of bubbles associated with Langmuir circulation, even though no surface manifestations were visible.

A forward‐pointing side‐scan sonar determined the “age” of bubble clouds after their generation by breaking waves. There is enhanced turbulent dissipation in the bubble clouds, and the dissipation rate close to the surface exceeds that predicted using conventional calculations based on the law of the wall and buoyancy flux. The correspondence between bubbles and turbulence implies a horizontally patchy turbulent structure near the surface. Below the base of the bubble clouds the distance between turbulent patches increases and is much greater than that of the bubble clouds. The submarine provides an excellent platform for multi‐sonar near‐surface studies.     

Different Turbulent Regimes and Vertical Turbulence Structures of the Urban Nocturnal Stable Boundary Layer

Turbulence in the nocturnal boundary layer(NBL) is still not well characterized, especially over complex underlying surfaces. Herein, gradient tower data and eddy covariance data collected by the Beijing 325-m tower were used to better understand the differentiating characteristics of turbulence regimes and vertical turbulence structure of urban the NBL. As for heights above the urban canopy layer(UCL), the relationship between turbulence velocity scale(V_TKE) and wind speed(V) was con...     

On Reynolds Averaging of Turbulence Time Series

We show that validity of Reynolds averaging for estimating the (ensemble) mean of a turbulence time series requires that the series values be both stationary and uncorrelated. In strict statistical terminology, these two conditions are jointly designated as independent identically distributed (i.i.d.). Moreover, we show that when the series values are correlated, knowledge of the correlation between the values is needed to obtain a reliable estimate of the mean. Last, we contend that a viable averaging algorithm must be Reynolds number (Re) dependent, requiring one version for low Re (Gaussian) turbulence and another for high Re (non-Gaussian) turbulence. Alternatively the median (as opposed to the mean) is recommended as a measure of the central tendency of the turbulence probability density function.     

Intermittent Bursting of Turbulence in a Stable Boundary Layer with Low-level Jet

The atmospheric stable boundary layer (SBL) with a low-level jet is simulated experimentally using a thermally stratified wind tunnel. The turbulence structure and flow characteristics are investigated by simultaneous measurements of velocity and temperature fluctuations and by flow visualization. Attention is focused on the effect of strong wind shear due to a low-level jet on stratified boundary layers with strong stability. Occasional bursting of turbulence in the lower portion of the boundary layer can be found in the SBL with strong stability. This bursting originates aloft away from the surface and transports fluid with relatively low velocity and temperature upward and fluid with relatively high velocity and temperature downward. Furthermore, the relationship between the occurrence of turbulence bursting and the local gradient Richardson number (Ri) is investigated. The Ri becomes larger than the critical Ri, Ri_cr = 0.25, in quiescent periods. On the other hand, the Ri number becomes smaller than Ri_cr during bursting events.     

On the effects of vertical eddy viscosity on rossby and eady waves in the ocean

The effects of vertical eddy viscosity on simple mesoscale waves in the ocean are studied. The decay of Rossby waves is investigated by one-dimensional depth-dependent linear stability problems which are derived for the interior non-viscous or viscous quasigeostrophic flow using parameterizations of the top and bottom boundary layers corresponding to Ekman suction, no-stress and bottom-stress boundary conditions.The non-slip condition at the bottom yielding an O(E_v^1/2)-Ekman layer causes very short damping times for the 0th Rossby mode. This suggests that this boundary condition is not suitable for mesoscale wave studies, because a Rossby wave fit for the MODE eddy can be done satisfactorily without any damping. Reasonable results for damping times of Rossby waves are obtained by prescribing the bottom stress, resulting from the constant-stress layer at the bottom, and the free-slip condition at the surface. The growth rates of Eady waves are reexamined using this bottom-stress condition.Vertical viscosity in the interior of the ocean, e.g. internal wave induced viscosity, may have a significant influence on the dynamics of the mesoscale motions, comparable to that of the boundary layers in some cases. The results are compatible with the sparse observations available.     

Experimental studies of the development of quasi-two-dimensional turbulence in stably stratified fluid

Quasi-two-dimensional turbulence was generated by towing an array of vertical cylinders through a tank which was filled with a two-layer stratified fluid. Sugar and Epsom salts were used, to give matching refractive indices for the two layers. The interface between the two layers was seeded with approximately 1000 neutrally buoyant particles. The evolution of this quasi-two-dimensional turbulence was visualized by photographing the fluorescent particles illuminated by a horizontal laser sheet traversing in the vertical direction. The three-dimensional particle velocity was obtained by digitizing the streaks. The evolution of the velocity correlations, length scales, one-dimensional and two-dimensional velocity and vorticity spectra were obtained for N = 5.72 s⁻¹, N = 4.43 s⁻¹, and N = 2.55 s⁻¹ (where N is the Brunt-Väisälä frequency). The results showed the physical process of inverse energy cascading and the formation of dominant vortical structures under the influence of density stratification. Compared with idealized two-dimensional turbulence, the flow is highly dissipative at high N, as a result of the frictional dissipation between the interface and the unstratified layers.     

Energy- and Flux-Budget Turbulence Closure Model for Stably Stratified Flows. Part II: The Role of Internal Gravity Waves

We advance our prior energy- and flux-budget (EFB) turbulence closure model for stably stratified atmospheric flow and extend it to account for an additional vertical flux of momentum and additional productions of turbulent kinetic energy (TKE), turbulent potential energy (TPE) and turbulent flux of potential temperature due to large-scale internal gravity waves (IGW). For the stationary, homogeneous regime, the first version of the EFB model disregarding large-scale IGW yielded universal dependencies of the flux Richardson number, turbulent Prandtl number, energy ratios, and normalised vertical fluxes of momentum and heat on the gradient Richardson number, Ri. Due to the large-scale IGW, these dependencies lose their universality. The maximal value of the flux Richardson number (universal constant ≈0.2–0.25 in the no-IGW regime) becomes strongly variable. In the vertically homogeneous stratification, it increases with increasing wave energy and can even exceed 1. For heterogeneous stratification, when internal gravity waves propagate towards stronger stratification, the maximal flux Richardson number decreases with increasing wave energy, reaches zero and then becomes negative. In other words, the vertical flux of potential temperature becomes counter-gradient. Internal gravity waves also reduce the anisotropy of turbulence: in contrast to the mean wind shear, which generates only horizontal TKE, internal gravity waves generate both horizontal and vertical TKE. Internal gravity waves also increase the share of TPE in the turbulent total energy (TTE = TKE + TPE). A well-known effect of internal gravity waves is their direct contribution to the vertical transport of momentum. Depending on the direction (downward or upward), internal gravity waves either strengthen or weaken the total vertical flux of momentum. Predictions from the proposed model are consistent with available data from atmospheric and laboratory experiments, direct numerical simulations and large-eddy simulations.     

Influence of foliar density and thermal stability on profiles of Reynolds stress and turbulence intensity in a deciduous forest

Observations were made of turbulence in an extensive deciduous forest on level terrain using a vertical array of seven three-dimensional sonic anemometer/thermometers within and above the canopy. Data were collected through the period of leaf fall and over a range of thermal stabilities. A bulk canopy drag coefficient was nearly independent of the density of the forest but decreased greatly with the onset of nocturnal stability. The depth of penetration of momentum into the forest increased with leaf fall but, again, was greatly curtailed by stable conditions. Turbulent velocities decreased with increasing depth in the forest but relative turbulence intensities increased to mid-canopy levels. Leaf density influenced turbulence levels but not as strongly as did thermal stability. Thermal effects were adequately described by the single parameter h/L, where h is the canopy height and L is the Monin-Obukhov length. The longitudinal and vertical velocity correlation coefficient was larger in magnitude than expected in the upper layers of the forest but decreased to a small value in the lowest layers where the Reynolds stress was small. The ratio _w /u ^*, where u ^* is the local friction velocity, reflected changes in the uw correlation, becoming smaller than usual in the upper canopy layers. It is believed that these effects result from the intermittent, spatially coherent structures that are responsible for a large fraction of the momentum flux to the forest.     

Acceleration effects for linearly-stratified flow over long ridges

Summary The time-dependent motion of long ridges through a linearly stratified fluid otherwise at rest is investigated in a series of laboratory experiments. Similarity conditions for relating such flows to the atmosphere are deduced from the equations of motion and boundary conditions for the respective systems.Experiments concerning end-wall effects in towing experiments with linearly stratified fluid systems are conducted. For obstacles extending across the entire width of the tow tank it is shown that the upstream conditions are continually changing so that a final steady state motion may never be realized. Isolated topographies are shown to induce significantly less effect on the far upstream fluid motions. Case studies for the flow past long ridges for which the motion at large times is to be that of single, double and triple mode lee-waves and breaking lee vortices are conducted for impulsively started and uniformly accelerated and decelerated obstacle transverses. The final flow configuration under certain situations is shown to be relatively insensitive to the starting conditions. In other cases the final flow can be highly dependent on the time history of the ridge traverse through the tank. For example, for the case in which a breaking lee vortex is expected as the final flow, small initial uniform accelerations from a zero velocity lead to the formation of a strong rotor along the free surface of the tank and in the lee of the obstacle. This rotor is maintained in an approximate equilibrium position as the ridge speed reaches a value for which a breaking lee vortex (having no rotor) should be expected; i.e., the type of flow obtained for impulsively started or rapidly accelerating ridges, other parameters being fixed.The phenomenon of the oscillation of the structure of the wake flow between a relatively smooth laminar lee-wave pattern and lee waves that break into turbulence is investigated for impulsively started ridges. By defining the parameterN _w as the number of waves downstream of the first trough that are clearly identifiable it is shown that the tendency for wake breakdown into turbulence increases with increasing internal Froude number, other parameters being fixed. No definitive period was found relating the alternating nature of the wake between breakdown, into turbulence, relaminarization and so on.With 20 Figures